WASHINGTON — Senate Majority Leader Harry Reid on Tuesday declared politically dead the effort to ban military-style assault weapons, a setback for President Obama and gun-control advocates who are pushing the Senate to move quickly on bills to limit gun violence.

Reid, D-Nev., is preparing to move ahead with debate on a series of gun-control proposals when the Senate returns from a two-week Easter recess in early April. Although he has vowed to hold votes on measures introduced after the Sandy Hook Elementary School massacre in Newtown, Conn., in December, Reid told reporters Tuesday that the proposed assault-weapons ban isn’t holding up against Senate rules that require at least 60 votes to end debate and move to final passage.

The proposed ban, “using the most optimistic numbers, has less than 40 votes. That’s not 60,” Reid said.

Still up for consideration are three other bills approved last week by the Senate Judiciary Committee: bipartisan legislation to make gun trafficking a federal crime, a bipartisan measure to expand a Justice Department grant program that provides funding for school security, and a Democratic proposal to expand the nation’s gun background check program.

Reid is working to determine whether to merge the three remaining bills into one comprehensive package, or to hold separate votes on each measure, said aides familiar with ongoing negotiations. The decision will be based on whether one or all of the bills receive sufficient support to ensure final passage, they said.

“I want people to have the ability to vote on assault weapons, mental health, safety in schools, federal trafficking, clips — everything,” Reid told reporters. “But I cannot do that until I get a bill on the floor, and it’s been very clear that the Republicans want us to have bills coming to the floor that have gone through committee.”

The assault-weapons ban is the most ambitious and controversial proposal backed by Obama. Introduced by Sen. Dianne Feinstein, D-Calif., the bill would ban almost 160 specific semiautomatic weapons and rifles and assorted military-style parts and also limit the size of ammunition clips to 10 rounds, banning larger rounds used in some of the more recent and brazen mass shootings. The ban has 22 other Senate Democratic co-sponsors, including Feinstein.

A bill limiting the size of ammunition clips was originally introduced by Sen. Frank Lautenberg, D-N.J., but was merged with Feinstein’s measure and approved by the judiciary panel.

Feinstein said Tuesday that Reid has assured her that the assault-weapons ban will earn an up-or-down vote in the full Senate, probably as an amendment to one of the other bills under consideration. A separate up-or-down vote can then be held on the ammunition clip proposal, she said.

“Obviously I was disappointed,” Feinstein said Tuesday, but she acknowledged that including her bill in any comprehensive package would sink the prospects of passing gun-control legislation this year.

“The enemies on this are very powerful, I’ve known that all my life,” she added, referring to the National Rifle Association. “But I’m confident this bill would be constitutional.”

White House Chief of Staff Denis McDonough said in an interview with CNN on Tuesday that Senate Democrats’ decision is not a setback for Obama’s gun-control efforts. He said that the bill can still be brought up as an amendment and that there should still be a concerted effort to pass it.

“We’re going to work on this. We’re going to find the votes,” McDonough said, according to a transcript. “And it deserves a vote and let’s see if we can get it done.”

Still unresolved is whether Democrats can secure Republican support for expanding the gun background-check program. Sen. Charles Schumer (N.Y.) is working with other Democrats to find potential GOP co-sponsors for a revised bill that would permit exceptions for firearm exchanges between family members or close friends. But talks have been hampered by disagreements about whether to establish a recordkeeping system for non-commercial gun transactions.

Mark Glaze, director of Mayors Against Illegal Guns, said gun-control advocates are hoping that Sen. Tom Coburn, R-Okla., will give what Glaze called his “hyper-conservative” stamp of approval to the background-check proposal.

“That would give a lot of moderate Democrats and other Republicans some cover, which for whatever reason they feel we need, but if not we press on,” Glaze said. “Of all the gun measures under consideration in the Senate,” he added, universal background checks remain “the biggest policy fix with the greatest public support and the most momentum.”

Nine in 10 Americans support expanding the nation’s background-check program, according to a recent Washington Post-ABC News poll.

As Congress prepares to leave for a recess, the White House is quietly coordinating with advocates to ensure that they remain united in message and focus as they lobby senators of both parties who have not taken a public stand on the issue, according to people familiar with the talks.

Glaze said his group, founded by New York Mayor Michael Bloomberg, an Independent, has hired several dozen field operatives and sent them to states where polling shows overwhelming support for an expanded background check program, including Arizona, Colorado, Georgia, Indiana and Nevada.

As part of its outreach, Glaze said the group plans to mobilize more than 900 mayors and hundreds of police chiefs and shooting survivors to stage events in congressional districts aimed at pressing lawmakers to support background checks. The group is planning a “national day of action” on March 28 that will include petition drives, rallies and news conferences.

The objective, Glaze said, is “to pound the point home on these members that their constituents are watching and if Congress can’t find a way to support a reform that has the support of 90 percent of the public, that’s going to be a pretty hard decision to defend.”

Separately, Organizing for America, an Obama-backed advocacy group, is planning its own day of action on March 28 to galvanize support around the gun-control proposals, a spokesman said.

Sen. Richard Blumenthal, D-Conn., who is co-sponsoring Feinstein’s assault-weapons ban, said that personal stories from the victims of gun violence are resonating most effectively with his colleagues.

“I think we have growing momentum on our side,” he said. “Newtown was a call to action and I think we’ve made tremendous progress. Three-plus months ago, this issue was politically untouchable. This time is different.”